11.3.1 GPS Heighting

INTRODUCTION


"...the geoid is that level surface of the earth's gravity field coincident with Mean Sea Level in an average sense..."


The italicised phrase in the above formal definition of the geoid emphasises the fundamental tension between the notion of the geoid as a real, but elusive surface, which plays a central role in classical geodesy on the one hand, and the utilitarian definition as a datum for heights required by practising surveyors on the other.

The geometric relationship between the reference ellipsoid -- the datum for ellipsoidal heights -- and the geoid is illustrated in Figure below, and defined by the simple equation:

N = h - H (11.3-1)

where N is the geoid-ellipsoid separation, or simply the geoid height, h is the ellipsoidal height and H is the orthometric height.



Figure 1. Relationships between ellipsoidal, orthometric and geoidal height for single point and relative heighting.

Geoid height is also a function of:

to which it is being referred (Figure 2). This illustrated, for a small network in Sydney, in the Table below. The same geoid model (based on the OSU89A geopotential model) is "mapped" on both the WGS84 geocentric ellipsoid, and the Australian National Spheroid in relation to the Australian Geodetic Datum (for a non-geocentric location for the ellipsoid centre).

Absolute geoid heights are not very accurate ...

Relative geoid heights can be accurate at the few ppm level.

ELLIPSOID:

 

  • Mathematical definition
  • Simple geometrical surface described by a few parameters
  • Cannot be "sensed" by instruments

GEOID:

 

  • Physical (gravitational) definition
  • Complicated surface described by infinite number of parameters
  • Can be "sensed" by geodetic instruments


The Sydney GPS network, OSU89A geoid on different ellipsoid and datum.
Name Latitude Longitude NWGS84 NAGD
B402

S33 54' 56.567"

E151 13' 52.399"

22.454

14.459

BOTY

S3358'23.355"

E15114'10.566"

22.217

14.376

CETS

S3355'05.557"

E15113'57.743"

22.443

14.452

CPDH

S3355'06.198"

E15114'03.196"

22.440

14.448

G106

S3355'13.377"

E15113'56.767"

22.435

14.451

GLEB

S3352'15.439"

E15111'05.280"

22.679

14.624

KYMA

S3356'45.707"

E15109'39.054"

22.448

14.640

LAKE

S3356'18.011"

E15112'40.436"

22.398

14.496

MBTS

S3356'28.596"

E15115'53.198"

22.297

14.325

MMCH

S3351'33.954"

E15113'18.439"

22.679

14.539

PETE

S3354'36.572"

E15110'31.635"

22.551

14.621

Q744

S3354'02.521"

E15115'03.756"

22.485

14.419

Q855

S3354'01.506"

E15114'56.739"

22.489

14.425

ROSE

S3354'49.779"

E15112'18.046"

22.498

14.535

UNSW

S3355'08.060"

E15113'52.148"

22.442

14.456

UU33

S3355'02.962"

E15113'40.084"

22.452

14.467

WBTS

S3351'10.704"

E15117'09.094"

22.618

14.367


NWGS84 mapped on ellipsoid a = 6378137.0 ; f-1 = 298.257223563
NAGD mapped on ellipsoid a = 6378160.0 ; f-1 = 298.25

Coordinates of AGD ellipsoid centre relative to WGS84 ellipsoid centre are assumed to be: X = 116m, Y = 50m, Z = -142m



Figure 2. Geoid height in relation to different ellipsoids and datums.

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© Chris Rizos, SNAP-UNSW, 1999